These are all essentially dynamic ways to get the correct connection string from your web.config file. As you know, you can have more than one connection string configured in your web.config/connectionStrings section.

By placing a key in the appSettings section for a selected connection string you want to use specifically, you are telling your DataObjects factory which connection string you want to use. This is a cleaner way of getting the connection string, in my opinion, than hard-coding the connection string name in your factory class, or by identifying it by it's index.